WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 13, 2014
Notes on a Particular Class of Perfect Cuboids
Author: Valeriu Dragan
Abstract: The current paper deals with the problem of the perfect cuboid, in particular with cuboids having only two of its edges even numbers. It is shown that in this particular class, a discussion can be made and some conclusions can be drawn to limit the existence of the perfect cuboid. In this paper Euclids formalism is used to generate Pythagorean triangles that define the faces of the cuboid. Because the pairs, (a; b); (c; d); (u; v), used to generate the triangles were not assumed to be relative primes, the triangles are not necessarily primitives. A computerized algebraic solver is used to solve the equations which were then compared with the numerical solutions obtained independently. Further generalization is required in order to extend the conclusions of this paper to a broader class of possible cuboids.
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Keywords: Perfect cuboid, Euler brick, Euclid equation, Pythagorean triangles
Pages: 811-819
WSEAS Transactions on Mathematics, ISSN / E-ISSN: 1109-2769 / 2224-2880, Volume 13, 2014, Art. #79